Welcome to the lore forum
@Lucifer. Bear with me, since I'm pretty rusty, so we may both look foolish here.
Is it literally meant that no living man may kill/hinder him? Is the specificity of 'living' important?
That seems to be the big question and Tolkien having a little Shakespeare-inspired
Macbeth with a prophecy. Does that mean someone who was a "living man" could have killed the Witch-King? What's the meaning of the 'prophecy?' Well, it started by something Glorfindel stated to the King of Gondor, Earnur:
"Do not pursue him! He will not return to this land. Far off yet is his doom, and not by the hand of man will he fall." These words many remembered; but Earnur was angry, desiring only to be avenged for his disgrace. Appendix A: Gondor and the Heirs of Anarion
In the T.A. 2050 Earnur rides off to Minas Morgul to answer the challenge of the Witch-King and is lost forever.
Glorfindel says
"not by the hand of man will he fall." The Witch-King says
"No living man will hinder me." So perhaps there's a game of telephone going on, where the message gets distorted down the line. It's interesting that it's said the Witch-King feared the ruling Steward Boromir:
Boromir son of Denethor (after whom Boromir of the Nine Walkers was later named) defeated them and regained Ithilien; but Osgiliath was finally ruined, and its great stone-bridge was broken. No people dwelt there afterwards. Boromir was a great captain, and even the Witch-King feared him. He was noble and fair of face, a man strong in body and in will, but he received a Morgul-wound in that war which shortened his days, and he became shrunken with pain and died twelve years after his father. Appendix A: The Stewards
Around T.A 2043 Glorfindel tells Earnur not by the hand of man will the Witch-King fall.
In T.A. 2475 Osgiliath is ruined, it is said the Witch-King feared a living man (the ruling Steward Boromir). But Boromir is dealt a Morgul-wound by the Witch-King and dies from it, T.A. 2489. Perhaps after killing a man he feared, the Witch-King feels more arrogant, and boastful. So, come TA 3019 (over 900 years after Glorfindel's prophecy) at the Battle of Pelennor Fields the Witch-King claims
"no living man may hinder me."
I don't think this answers your specific question, may even leave us with more questions, but just to provide a bit of context for how this all began.